# Invariant differential operators on H-type groups and discrete components in restrictions of complementary series of rank one semisimple groups

- Authors:
- DOI:
- 10.1007/s12220-014-9540-z
- Abstract:
- We explicitly construct a finite number of discrete components in the restriction of complementary series representations of rank one semisimple groups $G$ to rank one subgroups $G_1$. For this we use the realizations of complementary series representations of $G$ and $G_1$ on Sobolev spaces on the nilpotent radicals $N$ and $N_1$ of the minimal parabolics in $G$ and $G_1$, respectively. The groups $N$ and $N_1$ are of H-type and we construct explicitly invariant differential operators between $N$ and $N_1$. These operators induce the projections onto the discrete components. Our construction of the invariant differential operators is carried out uniformly in the framework of H-type groups and also works for those H-type groups which do not occur as nilpotent radical of a parabolic subgroup in a semisimple group.
- Type:
- Journal article
- Language:
- English
- Published in:
- Journal of Geometric Analysis, 2016, Vol 26, Issue 1, p. 118-142
- Main Research Area:
- Science/technology
- Publication Status:
- Published
- Review type:
- Peer Review
- Submission year:
- 2016
- Scientific Level:
- Scientific
- ID:
- 271146672